Oil-based varnishes are more durable than water-based types, and the more coats of varnish you apply, the stronger the finish. While this might not be a major consideration if you're decoupaging a wall hanging or picture frame, durability does matter when decoupaging furniture that will receive heavy use.
The process for applying oil- and water-based varnish is the same -- brush the varnish on, allow it to dry, sand it slightly, and add another coat. However, the two products behave somewhat differently.
Oil-based varnishes go on smoothly, but they are slow to dry and can accumulate dust. Water-based varnishes dry quickly, but the dried finish might contain bubbles or brush marks.
A heavily decoupaged piece might hide any imperfections, but oil-based varnish is more forgiving for the beginner.
Clean up is the one area where water-based varnishes are the obvious winner. To clean up oil-based varnishes, you'll need a solvent, such as mineral spirits.
Brushes are soaked in the mineral spirits and then dried. To clean up water-based varnishes, simply run brushes and trays under running water.
Water-based varnishes have fewer solvents, making them safer for the environment and your health.
Oil-based varnish is probably the best choice for most decoupage projects. It resists water damage and dries to a clear, hard shine that will protect the decoupage from scratching or peeling off.
When choosing a varnish, though, avoid oil-varnish blends, which contain tung or linseed oil that penetrates the wood but doesn't provide the hard, clear coating needed to protect decoupage.